I have to differ from most of the group here, although I think the links given to you by Jim Hanks are perfect for what you're trying to do. Solid wood/top ukes are great, of course, but there's a tradeoff to everything, and other things to consider. Since this will be your 'only' uke (unless you hijack you're daughters soprano), you may not want one you need to pamper, one you can take traveling without having to worry too much, one you don't have to rush into the humidity-controlled case (depending on your climate). If a laminate (either solid top or all laminate) uke is set up with good intonation, and is from a reliable manufacturer, you should have a good solid uke that lasts you a long time, and is pleasant to play. And if you drive through the desert with it in the back of the car, you won't be likely to get home to find cracks or warps, parted seams, etc.
Tenors are a good all-around size; as you start fingering notes and chords up the fretboard, adult-size fingers have an easier time...I notice even with concerts that at times it gets a bit cramped on the higher frets, and clear notes can suffer. Baritones...they're fine but traditionally tuned different and sound different than the other ukes, so unless you really want the large size and boomier bass, I'd stick with the tenor for now (you can always get a low G string or buy one that already has low G, if you prefer the linear tuning).
The Kalas, Islanders and others listed on that ukulele site page are all reliable instruments that will be intoned well, set up properly, backed up by the seller and the factory, and shouldn't have any surprises like warping or splitting as time goes by. That's a good set of attributes for a good solid first uke that you can enjoy playing. While you will get a million recommendations of everyone's favorite brand solid wood uke that may not cost a lot more, you may not enjoy the same benefits, and the next guy will have had the same uke and not liked it.
Or, you can order an all-solid, beautiful-looking tenor uke from a Vietnamese seller with good ebay feedback, and if it arrives intact, find it has buzzing frets, a split seam, cracks, and a month later discover you've got a twisted neck. But at least it's solid wood. There's plenty of time to venture into new woods and manufacturers after you get more involved, but a good solid, basic no-headache uke is a good way to start.
